Sorry, I don't have a textbook recommendation. LNKS is pretty new and the Biros & Ghattas 2-part paper is very good. It has a survey of traditional reduced space methods (more in the book by Kelley below, but this book doesn't target fluid flow specifically). I know very little about problems with small design space. There are some recent papers (most/all involve Volkan Akcelik) an large-scale inversion of time-dependent problems (advection-diffusion of airborne contaminants, seismic inversion) which are too big to apply LNKS (>10^11 space-time unknowns). They have developed some multilevel preconditioners for the inverse operators which make the number of iterations manageable even when the design space is mesh-dependent (and >10^7 unknowns).